Related papers: Concentration and local smoothness of the averagin…

This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…

This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…

We establish convergence results for a spatial semidiscretization of Mean Curvature Flow (MCF) for surfaces with fixed boundaries. Our analysis is based on Huisken's evolution equations for the mean curvature and the normal vector, enabling…

This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…

We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle…

This paper investigates a discretization scheme for mean curvature motion on point cloud varifolds with particular emphasis on singular evolutions. To define the varifold a local covariance analysis is applied to compute an approximate…

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve $\gamma$ in $\mathbb R^d$, $d\ge 3$. Despite the simple geometric structure of such curves, the sharp…

We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

We perform a geometric study of the equilibrium locus of the flow that models the diffusion process over a circular network of cells. We prove that when considering the set of all possible values of the parameters, the equilibrium locus is…

Particles are injected to a large planar rectangle through the boundary. Assuming that the particles move independently from one another and the boundary is also absorbing, we identify a set of abstract conditions which imply the local…

Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic…

We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…

Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…

We consider slowly time-dependent singular stochastic partial differential equations on the two-dimensional torus, driven by weak space-time white noise, and renormalised in the Wick sense. Our main results are concentration results on…